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Invertible Clipping for Increasing the Power Efficiency
of OFDM Amplification
Salvatore Ragusa, Jacques Palicot, Yves Louët, Christian Lereau
To cite this version:
Salvatore Ragusa, Jacques Palicot, Yves Louët, Christian Lereau. Invertible Clipping for Increasing
the Power Efficiency of OFDM Amplification. ICT 2006, 2006, Funchal (Madère), Portugal. �hal-
00083987�
Invertible Clipping for Increasing the Power
Efficiency of OFDM Amplification
Salvatore Ragusa, Jacques Palicot∗, Yves Louët∗, Christian Lereau
FranceTelecom R&D - TECH/ONE Laboratory 28, Chemin du Vieux Chêne - BP-98 38243 Meylan - France Email: Salvatore.Ragusa, Christian.Lereau@francetelecom.com
∗IETR/SUPELEC - Avenue de la Boulaie - BP-81127 35511 Cesson-Sévigné - France
Email: Jacques.Palicot, Yves.Louet@supelec.fr
Abstract— Large fluctuations of OFDM signal amplitude rep- resent an important problem for power amplification in mobile communication systems. In this paper, we propose a new Peak-to- Average Power Ratio (PAPR) reduction method based on the well known clipping and filtering one. Called "invertible clipping", it is performed thanks to a "soft clipping function". Since this soft clipping can be inverted in reception side, degradations are compensated. The derived method benefits from the advantages of classical clipping and filtering method and exhibits small computational complexity as compared to other peak reduction methods. In this paper, we show, thanks to extensive simulation results, that our method offers a global gain, greater than 1 dB.
That means that the power efficiency of the Power Amplifier (PA) increases of about 3.2% which corresponds to a PA consumption gain of about 10%.
I. INTRODUCTION
Multi-carrier transmissions and multiple access techniques including OFDM [1], BFDM [5] and MC-CDMA [4], have been receiving a widespread interest for wireless broad-band multimedia applications. Despite their popularity, these tech- niques have a major drawback, which is their high PAPR that results from the summation of multiple carriers with random phases.
This property has two consequences when these signals go through non-linear devices: first, an increase of the equivalent noise in the signal band, and second, an increase of the out of band signal power (the well-known spectral shoulders).
The problem of power amplification in multi-carrier systems is not new, but it still has not found a satisfactory solution and remains an important research problem. The most common approach today is to sufficiently back off the PA so that it operates in its linear region, which is far below the saturation point. This results in a significant amount of energy loss, generation of high temperatures due to the large power supply, and other disadvantages.
While this approach was acceptable for 2G systems, it is inappropriate for 3G and 4G systems, where power efficiency is a critical issue. Therefore, the problem of non-linear ampli- fication in multi-carrier systems is of major importance. Non- linear PA problems are encountered in most communication
Amplification function Transmitter side methods
Simple Down-compatibility
Yes No
Clipping
Additive Signal
Representation
Adaptative Processing
Yes No
Block scaling
Sub-carrier reduction
Coding
Sequences modifying Shaping
filter modifying
Multiple
Duplication SLM
Random Phasor
Selective scrambling Input signal
Fig. 1. Possible methods to carry out PAPR reduction
systems, including microwave links, satellite communication systems, radio-over-fiber links, magnetic recording devices and mobile communications. As pointed out earlier, the back off solution is usually adopted, but this approach is not satisfactory for future systems.
Since decades, many solutions have been proposed to solve this problem. Some of them compensate for non-linearities at the transmitter side and some of them carry out the processing at the receiver side. In this paper, we focus our attention on the transmitter side. As represented in Fig. 1 we have first to distinguish between processing on the amplification function and processing on the signal itself.
Here we are interested in working on the signal itself.
Another very important criteria employed to classify methods is the down-compatibility, i.e. methods which do not modify the baseband signal and those which modify it. Among the techniques which modify the baseband signal, we can find Selective Mapping (SLM) [2], Reed-Muller channel coding [3], Partial Transmit Sequences (PTS) [8], etc... . Nevertheless, they have a high computational complexity as major drawback.
There are only a few techniques which are down- compatibles. Among them we find clipping with filtering [7]
and tone reservation [11]. This clipping technique is very
simple to implement, but it requires a low Clipping Ratio (CR) to achieve a significant PAPR reduction. As a consequence, non-linear problems come out again. Out of band problems are eliminated by filtering, but the in band noise deteriorates the Bit Error Rate (BER). The down-compatibility property is ensured only when the increase of BER due to clipping is small [9].
In this paper, we show that it is possible to increase the power efficiency of the PA when it is used with OFDM signals.
To derive this method, we start from the very simple technique previously cited (the "Clipping and Filtering" method) with which we associate an old one, well known in the automatic domain [10]. This method is illustrated in Fig. 2, and it could be summarized by stating that it is always possible to hide a non-linear function with another one which is invertible. We use an appropriate soft clipping function, which is invertible in the definition domain. This is the starting point of our
"invertible clipping" method.
The paper is organized as follows: in section II, we de- scribe our technique, the invertible clipping, then in section III simulation results are provided, using the OFDM IEEE 802.11a example [6]. This section is divided in two subsections that show results without and with Additive White Gaussian Noise (AWGN). In section IV, the results prove that the overall system gain, from the amplifier point of view, can reach an Input Back-Off (IBO) of 1 dB. Finally, in section V we give some conclusions to this work.
II. INVERTIBLECLIPPING
A. Principle
The clipping function before non-linear amplification re- duces the power dynamics (i.e. PAPR) of the output signal. It works as a sort of masking to the PA’s non-linear characteristic.
What will be done is to hide the amplifier’s non-linear charac- teristic by a more severe one in term of non linear distortions.
The principle of our new clipping method is derived from the classical clipping. Unlike the classical one, the non- linear clipping function (soft clipping function) is inverted in reception. This allows to compensate the non-linear distortions introduced in the clipped signal’s useful band, thus improving the received signal’s quality and BER performance.
Therefore, for the same clipping threshold and Eb/No=10 dB, BER due to the classical clipping method is equal to 4.19 · 10−1 while BER for the invertible clipping one is equal to1.57 · 10−2.
Fig. 2 shows PA masking and the principle of the soft invertible clipping. Thus, our proposed method is based on:
• Soft clipping functionwhich is a stronger non-linear func- tion than the PA’s one and it is placed on the transmitter side. This function should be invertible in the definition domain of the transmitted signal.
• Filtering functionto obtain the required Adjacent Channel Power Ratio (ACPR) value. This filter does not increase the complexity because in practice it will be performed by a shaping channel filter of IEEE 802.11a OFDM modulation.
Soft clipping PA
»
Maskingf(x)
Soft clipping PAPA
»
Maskingf(x)
f-1(x)
+
InversionMasking
=
Linearf-1[f(x)]=x f-1(x)
+
InversionMasking
=
Linearf-1[f(x)]=x
Fig. 2. PA masking and invertible clipping principle
−0.25 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25
−0.25
−0.2
−0.15
−0.1
−0.05 0 0.05 0.1 0.15 0.2 0.25
Invertible clipping function
x
f(x)
Linear Poly Poly Inv
Fig. 3. Invertible clipping function (polynomial) and its inverse
• Inverse non-linear functionon the receiver side.
Given the signal x(t) to be clipped, clipping is carried out through a saturation function y = fP(x) that has a certain saturation level ysat for which x(t) = xsat. The considered function fP(.) has to be increasing monotone and positive in the x(t) domain.
fP has been chosen as a polynomial function for the invertible clipping method (see Fig. 3). It is an odd func- tion of fifth order because the even order InterModulation products (IM n), generated by an even polynomial order, are eliminated by the filter and those greater that order n = 5, are very small in amplitude. The {ai} coefficients of fP
are calculated to achieve the clipping (saturation) threshold ysatfor a Clipping Ratio (CR) equivalent value. The inverted function fP−1 is deduced from fP. In Fig. 3 its characteristic fP(x) = a1x+ a3x3+ a5x5 is shown.
The CR is defined as the ratio in voltage between the saturation level (ysat) and the OFDM signal’s mean square value (Vrmsof dm):
CR= ysat
Vrmsof dm
(1)
The IBO represents the input power gap between the mean power of the signal that has to be amplified (Pmin) and the amplifier’s saturation power (Psatin):
IBO [dB] = Psatin [dBm] − Pmin [dBm] (2)
5 6 7 8 9 10 11 12 10−3
10−2 10−1 100
Prob(PAPR > value)
PAPR [dB]
CCDF(PAPR)
Classical OFDM Invert. Clipp. (CR=0.9) Invert. Clipp. (CR=1.2) Invert. Clipp. (CR=1.5)
Fig. 4. CCDF of the PAPR
B. Effects on signals
At the transmitter side, the invertible clipping method reduces the amplitude dynamics, and thus the PAPR of the signal that has to be amplified. This result is presented in Complementary Cumulative Distribution Function (CCDF) terms which is defined as follows:
CCDFP AP R(papr) = P rob[P AP R > papr] (3) This function represents the probability that the PAPR of the OFDM signal exceeds the threshold papr.
This invertible clipping method allows to reduce the PAPR of the OFDM signal. Fig. 4 shows PAPR’s CCDF for classical OFDM signal and for clipped signal using different values of CR = [0.9, 1.2, 1.5]. Here the CCDF of PAPR after clipping decreases slowly, compared to the classical clipping because the invertible clipping function reaches more slowly the saturation level. Thus, PAPR reduction for a CCDF value of10−2 is equal to 2.0, 1.5 and 1.0 dB for a CR value of 0.9, 1.2 and 1.5 respectively. The gain of invertible clipping for a CR value of 0.9 is equivalent to the gain of classical clipping for a CR value of 1.5.
Unfortunately, clipping generates a spectral regrowth (the so called spectral shoulders) on the spectrum of output signal, widening its frequency support. Thus, parasitic frequencies appear in the adjacent channels. Filtering after clipping is therefore compulsory to limit this spectral regrowth and, finally, to assure a good system performance in ACPR terms.
Fig. 5 shows the ACPR degradation due to high clipping (low CR values). If the clipping ratio increases, the degra- dation of ACPR diminishes and it tends to the value of OFDM signal’s ACPR before clipping (−25.2 dB) without ever reaching it. Unlike classical clipping, even if the clipping function does not saturate the signal anymore, the global non- linear behavior of the invertible clipping function (see Fig. 3) always introduces distortions. This justifies that the asymptote of ACPR is higher than the ACPR value of classical OFDM signal.
0.5 0.7 0.9 1.2 1.5
−40
−35
−30
−25
−20
−15
ACPR vs Clipping Ratio (CR)
CR
ACPR [dB]
ACPR(OFDM) = −25.2 dB
Aft. Soft Clipp.
Aft. Filter
Fig. 5. ACPR versus CR
In the same figure we find the ACPR trend after filtering.
We see also the gain of filtering function. The ACPR reduction filter is a Nyquist filter with a bandwidth of 20 MHz and roll- off factor of 0.35 and it does not increase the complexity of this method. In practice, filtering will be performed by a shaping channel filter of IEEE 802.11a OFDM modulation.
With these first simulation results, the efficiency of invert- ible clipping and filtering on PAPR and ACPR respectively is evident. Now, we shall validate this PAPR reduction method for a complete transmission chain which includes also the PA.
III. SIMULATION RESULTS WITHPA
In this section we present BER performance of a general transmission system with an invertible clipping, a PA and an AWGN channel. Simulation results have been obtained for an OFDM system based on the IEEE 802.11a standard. The mapping employed is a 16-QAM and the number of sub- carriers is equal to 64 with a signal bandwidth of 20 MHz. The results are given for the three following measurements: ACPR, BER and Error Vector Magnitude (EVM), with a complete chain which includes the PA.
A. ACPR results with PA without AWGN channel
Fig. 6 shows that for clipping ratio values from1.5 to 0.9, there are 3 dB gain on the PA’s IBO for the same ACPR value (−29 dB). This may also be interpreted as a much more linear behavior of the PA.
B. BER with PA and without AWGN channel
In reception, after inversion and in presence of a noiseless channel, we measure the system performances for BER. Fig. 7 shows the achieved gain. Thus, for CR=0.9 and IBO=3 dB (high clipping zone in the figure), the BER decreases from 10−3 to 10−5. It is evident that the PA is hidden by soft clipping in this area. On the contrary, for a CR=1.5 (low clipping zone in the figure) the BER degradation is mainly due to the PA.
1 0 3 2
5 4 0.5
0.7 0.9
1.2 1.5
1.8
−35
−30
−25
−20
CR ACPR after PA vs CR_soft and IBO (alpha=0.35)
IBO [dB]
ACPR [dB]
−34
−32
−30
−28
−26
−24
−22
−20
ACPR = −29 dB
Fig. 6. Gain of 3 dB on the PA’s IBO
0 1
2 3
4 5
0.5 0.7 0.9 1.2 1.5 1.8 10−4 10−3 10−2 10−1
Before
After
IBO [dB]
BER before and After Inversion vs CR_soft and IBO (alpha=0.35)
CR
BER
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
Low Clipping
High Clipping
Fig. 7. Inversion effects on BER
C. BER and EVM results with AWGN channel
Fig. 8 shows BER after inversion versus CR and Eb/No.
Inverse function degrades BER performance of the system because it expands the channel additive noise. Thus, the BER value is of1.57 · 10−2 for CR=0.9 and Eb/No=10 dB.
Fig. 9 shows EVM versus IBO and the signal to noise ratio Eb/No. The invertible clipping function and its inverse have not been taken into account. An EVM improvement is obtained for high values of IBO and Eb/No (EVM=−14.3 dB). In this region, the PA becomes more and more linear and the noise power density decreases.
Then, for low values of IBO and Eb/No, a high EVM degradation appears because the PA saturates the OFDM signal and noise power density of the channel becomes important (EVM=−3.1 dB).
IV. GLOBALPERFORMANCES
The transmission system is composed of several functional blocks: soft polynomial clipping, filtering, PA, noise transmis- sion channel, and inversion. Each of these blocks influences
2 0 6 4 10 8 14 12 0.5
0.7 0.9
1.2 1.5
1.8 10−4
10−3 10−2 10−1
EbNo [dB]
BER after Inversion vs (EbNo, CR)
CR
BER
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Fig. 8. BER after inversion on the noise channel
0 1 2 3 4 5 0
2 4
6 8
10 12
14
−16
−14
−12
−10
−8
−6
−4
−2
IBO [dB]
EVM vs (IBO, EbNo)
EbNo
EVM [dB]
−14
−13
−12
−11
−10
−9
−8
−7
−6
−5
−4
Fig. 9. EVM measurement versus IBO and Eb/No
the global system with a positive or negative impact on its performances.
Now, we will determine IBO gain of the PA due to the presence of an invertible clipping system, which represents the main goal in this study. The invertible clipping reduces the amplitude dynamics of the OFDM signal realizing a PAPR reduction. Consequently, this allows to achieve an IBO gain.
Moreover the inversion of clipping function improves the qual- ity of the received signal, thus the BER system performance.
Unfortunately, the noise channel will degrade the perfor- mances of this new clipping method [§ III-C]. On the receiver side, the inverse function expands the channel additive noise.
Thus, IBO gain analysis will be performed for a global transmission system in presence of a noise channel approach- ing a realistic transmission context.
The PAPR reduction due to the invertible clipping has already been shown in Fig. 4. A reduction of 2 dB is obtained for a clipping ratio of 0.9 and a CCDF value equal to 10−2. This confirms the efficiency of the new clipping method to
0 2 4 6 8 10 12 14 10−3
10−2 10−1 100
IBO Gain for Invertible Clipping
EbNo
BER
Without Invert. Clipp. + IBO=6 With Invert. Clipp. + IBO=5
Fig. 10. Real IBO gain due to the invertible clipping
−250 −20 −15 −10 −5 0 5
5 10 15 20 25 30 35 40
PA Characteristic
Input Power [dBm]
Power Efficiency [%] Output Power [dBm]
Output Power Power Efficiency
Fig. 11. Power amplifier characteristic (output power and efficiency)
reduce amplitude fluctuations of OFDM signals.
To achieve IBO gain of the PA, the BER is measured versus Eb/No for an IBO value of 6 dB (the system includes the filter, the PA and the AWGN channel). Then, a simulation of the global system (soft clipping, filter, PA, AWGN channel and inversion) allows to calculate the BER versus Eb/No for CR and IBO values of 0.9 and 5 dB respectively (see Fig. 10).
Thus, Fig. 10 shows two BER measurements: without invertible clipping system and IBO=6 dB, and with invertible clipping system and IBO=5 dB. The two curves are the same.
After this result we can affirm that the invertible clipping system permits to gain 1 dB on IBO of the PA.
This IBO reduction has an impact on the power efficiency of the PA: from Fig. 11 (which is a typical example of a class AB PA for wireless applications), with a IBO gain of 1 dB, the efficiency grows from 23.8% to 27%, which represents about10% saving on the PA consumption.
V. CONCLUSIONS
The invertible clipping method assures a PAPR reduction keeping a high quality of the received signal thanks to the clipping function inversion. This technique is very simple to carry out. Unfortunately, ACPR raises in consequence of the non-linearities of the clipping function on the transmitter side, thus filtering is necessary in any case. The finality is a power consumption gain of the PA, and in our case we get about10%, which is considerable for embedded terminals. Further works will deal with the influences of a multi-path fading channel.
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